Question: Simplify; express your answer in exponential form. Assume $p\neq 0, x\neq 0$. $\dfrac{{(p^{5}x^{3})^{5}}}{{(p^{5}x)^{2}}}$
Solution: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(p^{5}x^{3})^{5} = (p^{5})^{5}(x^{3})^{5}}$ On the left, we have ${p^{5}}$ to the exponent ${5}$ . Now ${5 \times 5 = 25}$ , so ${(p^{5})^{5} = p^{25}}$ Apply the ideas above to simplify the equation. $\dfrac{{(p^{5}x^{3})^{5}}}{{(p^{5}x)^{2}}} = \dfrac{{p^{25}x^{15}}}{{p^{10}x^{2}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{25}x^{15}}}{{p^{10}x^{2}}} = \dfrac{{p^{25}}}{{p^{10}}} \cdot \dfrac{{x^{15}}}{{x^{2}}} = p^{{25} - {10}} \cdot x^{{15} - {2}} = p^{15}x^{13}$